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What's the meaning of the unit bivector i?@celtschk OK. But Hestenes maintains quaternions are just an aspect/transformation/... of the more general geometric algebra (at least in sofar they are used in Physics). I can't deduce any geometric meaning from quaternions either, so although insightful, it doesn't help me much (probably why you made it a comment anyways ;-)).

Jul31

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What's the meaning of the unit bivector i?OK. This is part of the meaning I get. The bivector as an operator is a rotor. But the bivector as basis element of the algebra should have a meaning on its own. Is my plane interpretation correct?

Jul31

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What's the meaning of the unit bivector i?It seems you avidly hate Hestenes' formulation. I get the parallel with $\gamma$ algebra the way you see it (I first came into contact with geometric algebra when studying the Dirac equation), but in the pdf referenced, he's not talking about $\gamma$ algebra, he's talking Euclidean geometry, where stuff like $\gamma$-matrices (he's not even talking about matrices) are not even relevant. You're giving a non-geometric interpretation IMHO, which is not quite what I'm after. I'm after the interpretation Hestenes describes.